Is it possible to make the f-curve noise modifier's scale into a variable?
Envelope modifier

EDIT: On re-readig the question this is more in regard to strength than scale.

Can add an envelope modifier after the noise modifier.

Set control points to expand or contract accordingly.

Example gif, add a control point limiting noise to [-1, 1] and then at frame 140 expand to [-10, 10]



For scale one method would be to add modifiers for a series of scales and frame ranges..  



For being able to animate the influence, consider using the NLA editor and keyframe the animated influence

How to apply fcurve modifiers on top of each other, like object modifiers?